We propose the first algebraic determinantal formula to enumerate random rhombus tilings filling a centro-symmetric octagon of any size. This result uses the GesselViennot technique and generalizes to any octagon a former specialized formula by Elnitsky.

Abstract. In this paper we enumerate the number of ways of selecting k objects from n objects arrayed in a line such that no two selected ones are separated bym−1, 2m−1, · · · , pm−1 objects and provide three different formulas when m, p ≥ 1 and n ≥ pm(k − 1). Also, we prove that the number of ways of selecting k objects from n objects arrayed in a circle such that no two selected ones are sepa...

A very detailed segmentation of prosodic phrase was carried out in order to construct a Japanese prosodic database. Boundaries correspond to junctures between phrases including C|C and V|V clusters. The "prosodic phrase" we introduced as a unit of the segmentation was defined and regarded as a unit of language speech perception. For the exact segmentation, the wide-band spectrum, the narrow-ban...

Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.

We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, i.e. generating function manipulations, we derive the complete asymptotic expansion. keywords. connected graphs, analytic combinatorics, generating functions, asymptotic expan...

The jump operator on the ω-enumeration degrees is introduced in [11]. In the present paper we prove a jump inversion theorem which allows us to show that the enumeration degrees are first order definable in the structureDω ′ of the ω-enumeration degrees augmented by the jump operator. Further on we show that the groups of the automorphisms of Dω ′ and of the enumeration degrees are isomorphic. ...

In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using the canonical construction path method and the homomorphism principle.

We develop a geometric approach to the study of (s,ms−1)-core and (s,ms+1)core partitions through the associated ms-abaci. This perspective yields new proofs for results of H. Xiong and A. Straub (originally proposed by T. Amdeberhan) on the enumeration of (s, s + 1) and (s,ms− 1)-core partitions with distinct parts. It also enumerates the (s,ms+1)-cores with distinct parts. Furthermore, we cal...

Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1. §

Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such presentation. We show that it is much easier than it rst appears, albeit at the ...